We have flown on them several times out of Buffalo to NYC and to MCO. I personally enjoy flying with them. Yes, they do have assigned seats. When you buy online, part of the process is to pick out your seats. They show an actual diagram of the plane with rows/seat numbers and what seats are available. I found the people to be extremely friendly and helpful. I generally fly Southwest because of the rates but I've received some wonderful deals on Jet Blue too. I like Jet Blue because they have more schedules operating in our area than SW.
My kids--they love the TV's at each seat. This is a huge, huge plus for our family. They like putting on their headsets and watching TV to kill the time. Not too many stations to choose from but enough to find something to watch for sure.
Let me say this for them--when my Mom passed away last year it was five days before we were due to leave for WDW. Obviously, we postponed our trip. I had lots and lots of trouble with WDW rescheduling at the rate I initially book (went just a few weeks later than originally scheduled). Now Jet Blue on the other hand, they were amazing. They let me rebook to any flight they had available despite the cost difference. The obviously had to confirm with the funeral home but that took just minutes and I was rebooked in less than 10 minutes. The kicker--the flights we picked to travel had gone up in price by almost $500 in total. We never paid a single penny! They were very understanding and sympathetic. Love this airlines!!!!!!